8 More Things I Learned at ISTE

I’ve only been to a couple of really large conferences. At these, it seems that keynotes are usually preceded by a local group of performers. Today’s keynote had a great local dance group, but that group was preceded by dancing robots. They even bowed at the end. Anyway, it was another fun filled day of learning. I’m exhausted and while I know my way around the convention center in Philadelphia now, it’s still overwhelming. Anyway, here are 8 more things I learned today.

Bring on the Dancing Robots

8 ) The keynote speaker today was Steven Covey author of The 7 Habits of Highly Effective People from a gazillion years ago. He was here to talk about leadership, especially in kids. On the website for his book The Leader in Me, Covey has the phrase – “Leadership is doing the right thing even when no one is watching.” During the keynote, he defined leadership as the communication of other people’s worth and potential. He then started to incorporate his 7 steps and use the terms skill sets, tool sets, and mindsets (of which the first two lead to incremental changes and mindsets lead to quantum leaps). Perhaps I’m too cynical, but hasn’t Covey written about these “7 habits” over and over again. This time he just melds Dweck’s work (without giving her credit) and uses the term mindset as the underlying foundation of his 7 habits. Don’t get me wrong. I think his habits are really applicable and relevant to both teachers and students; it’s just not exactly new and innovative. Nonetheless, I left with some great quotes and a good reminder of these seven habits:

“The best way to change the future is to create it.”

“Live life in crecsendo.”

“The main thing is to keep the main thing the main thing.”

He also mentioned how test scores are the “worst form of identity theft we can give [kids].”

7) I met some great teachers (one who is an NAIS teacher of the future), who are planning on putting on an EdCamp in May in Seattle. I’m diving head first into volunteering to organize. I actually only learned what an EdCamp is today for the first time and look forward to being part of the team. The video below explains it. A very cool way for teachers to share.

6) I learned of a math fact fluency program that is adaptive and individualized, can be used anywhere (classroom, lab, home), is easy for teachers to monitor progress and will save countless hours of photocopying fact sheets, correcting, and keeping track of something that should be an automated mindless task these days freeing up the teacher to analyze where the gaps are in the students’ memory of math facts. Reflex is the name of that program.

5) I learned about a free QR code generator at qrcode.kaywa.com. QR codes are those square barcode like symbols seen on this sidebar, that can be read with your camera on your mobile device. That one just takes you to this blog. There are some very cool applications for this.

4) Hitachi has a product to help simulate an interactive white board on your pre-exsisting one. Unlike ebeam, however, you don’t need a stylus (just your finger will do), you can have three kids up there simultaneously, and the multi-fingured and whole hand gestures are pretty cool. Priced at $750 it’s a fraction of the cost of SMART boards.  I also saw some great portable systems that help lower the interactive whiteboards so kids can use it – both the white board and the projector is mounted onto the cart. The interactive whiteboard wars are starting to shape up and there aren’t just two major players anymore. That’s good for everyone as long as people don’t get to set on each company’s proprietary software. It’s funny how most of the whiteboard demos, elementary, middle, or high, were designed with the teacher standing in front of the class and the class sitting and responding. I get that teachers will use that tool frequently, but I hope students actually get up there and are the ones interacting with the board. Below is a page from Samsung’s brochure. Notice the desks in rows and the students all sitting passively?

3) I learned that I still don’t know how so many companies are selling single use devices for outrageous sums when a $9.99 app on an ipad will do the same thing.

2) I went to an incredible session on how to develop global empathy in children. Some examples: Grandparents in Ireland reading to the class via skype or podcast. Using twitter hashtags, a middle school teacher found a few adult directors who were tweeting about various scenes. The kids who were directing their version of the play tweeted their directions and got feedback from adult directors in England.

1) The steps Rocky ran up to the Philadelphia Art Museum aren’t that arduous but make for a great scene in a movie. By the way, why is it that almost all attractions shut down the same time each day the conference is over?

View of the city from the top of the steps to the Philadelphia Art Museum

Learning WITH Your Students

We were very fortunate with our new school building to have a garden bed built for every grade. Integrating gardening into the curriculum would be one strand through which children would learn about sustainability. There was one small problem though: I didn’t know very much about gardening. So, when the year began, I promised my students that I would write a reflection on my blog for every journal entry they wrote. Seattle’s winter has been pretty miserable, so it’s been a while since we observed or wrote anything.

We learned about growing plants and food in many ways. We read non-fiction and fiction (I have a new appreciation for The Secret Garden), did some actual gardening, planted trees in a local park for our all-school service day, and most importantly learned from others. (One of our teachers is a master gardener, and we are lucky enough that she is also a school neighbor allowing us, not only the opportunity to learn from someone passionate about gardening, but also having  classes visit her own personal garden many times a year.) Just last week, we were in her garden measuring the perimeter of various beds with non-standard units of the children’s own feet. This led to a great discussion about standard and non-standard units for measurement.

We learned about the worm bins and compost bins (our fifth graders collect the compost from the classes once a week and add them to the bins). We also learned how to fertilize the soil using cover crops such as vetch and clover. Then, just before spring break, the two second grade classes planted some flowers, radishes, and a host of lettuce greens. This week, we took some time to observe our garden bed, think about all the garden related activities we did, and then write a journal entry. Next week, we should be ready to taste a few things.

I keep telling my students that learning never ends. I always learn from them as they have so much to teach, but to also have the opportunity to learn with them, is pretty special.

Repost: We Need More Patient Problem Solvers

I posted this about a year ago, and what I love is colleagues who say, “Hey did you see this?” I’m just really happy they are finding it their own way and sharing with everybody. That’s a very important reason why some educators blog, tweet, and whatnot.  It’s not about whether they read it then or not, it’s that it creates a culture of sharing and continued reflection and growth. I was very happy to see my colleague post this TEDx talk. (By the way, I’m headed to my first TEDx event in a few minutes. All about inquiry,  innovation, and identity through instruction. I can’t wait. I will share via twitter to try an encourage our faculty into the positive and responsible use of social media even more.) Twitter is how I scored the ticket to the event!

I’m not a big fan of text books. Good tools, perhaps and also convenient. Still, it doesn’t make us better teachers. Furthermore, textbooks in many ways dumb down ideas. In math, textbooks tend to encourage the “one way to get to the right answer” kind of questions. I was great at at decoding textbooks and thus was very successful in high school. But how does someone get an A in a subject like physics and have no clue how the world works? Kids really need to understand how things work rather than learn to manipulate formulas. Students have to come up with problems, reason, and have patience.

His wonderful TED talk explains the problem with math in this country today. Making math real is what it’s about. In second grade, when a child asks, “How many more minutes to recess?” resisting the temptation to tell them and saying instead, “There’s the clock,” provides a real need to learn how to do it.

When you dine with friends and its time to split the bill, it’s amazing how often people pull out their calculators to divide and then calculate the tip. Often they are the same people who knew how to use the quadratic equation at one time. Something is not right in the way math is taught. Hopefully, we as educators learn how to it better.

He’s got a good blog: http://blog.mrmeyer.com/

Where’s the Math

After doing my taxes this past weekend, I realized that I did so without doing any math. I just put numbers into various boxes and trusted the software to do the rest. Perhaps the only math involved was having a sense whether those numbers I was entering seemed reasonable. This made me start to wonder about the math most adults do in their daily lives. How many people use the quadratic formula in their daily lives? Yet, when they learned it, did they learn it in a valuable enough way, that with that new knowledge, they can think in a particular way? How many know that when there are six people dining and you split the bill evenly, leaving a 20% tip, all you have to do is just divide the bill by five and have the sixth person cover the tip? If your student is working on 3-digit by 3-digit subtraction and on a post-test makes many errors, can you tell what directly caused those errors?

I ask that last question because as a school we’ve been examining several math curricula. One of them has an incredible technology component that includes computer based assessments. It’s amazing how quickly you get data back and the teacher doesn’t even have to grade the paper. Easy, right? Upon further reflection though, a child who might still get about half the questions directly involving 3-digit by 3-digit subtraction wrong, the data would simply just indicate that. Without examining the scratch piece of paper, interviewing your student, or observing the child in action, you wouldn’t be able to isolate whether or not the error was a simple fact error, errors with regrouping, inversion, or even adding instead of subtracting. If you were able to isolate what that error was, though, imagine how quickly you could help that child develop.

This month’s issue of the journal, Teaching Children Mathematics, contains a few great articles. One is called, “Action Research Improves Math Instruction,” which features elementary school teachers who, as part of a course they’re taking, embark on a “practitioner-based” research process in their classrooms. One of them, a 3rd grade teacher, looked carefully at 3-digit subtraction, read about the kinds of common errors children make on questions like these and decided to make her students ‘subtraction detectives.’ They had equations that were already solved, some with errors, and they had to practice finding and describing the error. The improvement in her students’ assessments improved greatly. The teacher didn’t know whether this was a ‘best-practice’ but it made solid sense to her and she gave it a try. The article mentions that “Action research addresses specific student needs, targets classroom issues, keeps teachers current, and discourages ineffectual methods.”

This year, our school has been examining several different math curricula with one of its objectives being a common scope and sequence. Today, we had a faculty meeting discussing the pros and cons of the different curricula, and I found the discussion rich and robust. We also asked ourselves some very important questions. We didn’t come up with any immediate answers, but I was really impressed when colleagues disagreed with each other, how the discourse remained passionate, but civil, and everyone made extremely insightful and thoughtful comments. Everyone seemed to be aware of their own biases as they spoke. I wondered, leaving that meeting though, and re-reading this article, if we needed not only to think of a common set of expectations, but if we could also find ways to examine student progress even more carefully and identify where gaps lie, or how their learning can be enriched.

Another article in the same issue called, “Professional Development Delivered Right to Your Door.” It listed the following as Best Practices of Professional Development: Professional Development must be –

1. grounded in participant-driven inquiry, reflection, and experimentation;
2. collaborative, involving a sharing of knowledge among educators and a focus on teachers’ communities of practice rather than on individual teachers;
3. connected to and derived from teachers’ work with their students;
4. sustained, ongoing, intensive, and supported by modeling, coaching, and the collective solving of specific problems of practice;
5. related to other aspects of school change; and
6. engaging, involving teachers in concrete tasks of teaching, assessment, observation, and reflections that illuminate the processes of learning and development (Darling-Hammond and McLaughlin 1995).

Regardless what direction we go in math, I feel like we met all those goals. I think the process was, and will continue to be an ongoing one. I feel very fortunate to work at a school with such caring and passionate teachers.

 

Day 1 of Flipping the Classroom

There’s the common expression, “Change is hard. You go first.” Well, I’ve been doing a few firsts this past year or so, partly because I decided not to wait. If I think it’s worth experimenting with, I’ll try it. What I’ve learned is that with a few of these things, I might have been better off talking about it, rather than dive right in. As a result, I may have ruffled a few feathers here and there and had to repair a few work relationships. It was actually a good exercise in growth for me and made me a lot more reflective about what I want to do next.

I started this blog, for example to share what I learned at a conference, but decided to keep it going because I actually enjoy it. Because I had no expectation of anyone else blogging, I was oblivious to the fact that some might feel that they would have to share what they learned via a blog. It’s just my way, and I enjoy it. I also started my own classroom website because I couldn’t wait for our school’s official site to have all the features I wanted. It’s worked for me and my students’ parents and that’s really all it boils down to. There are so many ways to communicate, sometimes the purpose dictates they type.

Well, I’m at it again. After only a couple of weeks since the TED talk “Flipping the Classroom” aired, I unleashed Khan Academy upon my second graders. Honestly, the videos are pretty dry and boring for the most part, but the kids love the exercises, the immediate feedback, and the choice. One child decided for homework tonight to head to the geometry section which asks for the area and circumference of circles. He made a few attempts, got all them wrong and decided he’d come back another time. It was very non-threatening. Today was just the first day, we headed to the media lab so they could learn how to login and logoff. And even though I assigned about 10 to 20 minutes, I noticed that many kids were engaged enough to spend much more time on it. I’m actually more excited about the data that might come back after Spring Break. Why? So much of good math pedagogy is not just helping a child develop a concept, but asking the right questions. Knowing what children have mastered, allows you to target your questions more precisely. Of course good teachers who already know their students well do this, but with the added data, who knows.

One interesting unintended consequence occurred. Many of my students have older siblings. So far, I’ve gotten great feedback from parents, but they wanted to know how their older child could sign in. I told them how and that they could sign me up as their coach if they wished. This is a big experiment. I don’t intend to have students using Kahn Academy in class, but only at home. What I will do, is use the data to help inform the way I teach each child. As Kahn put it in his TED talk, “Flipping the Classroom.”

Kahn Academy approaches math in a very linear, sterile manner, but with some of the basic skills under their belt, they may be able to really grapple with project based learning activities which involve plenty of mathematical problems, creativity, and the beauty of math that doesn’t always get to see the light of day the way our math texts are written. Who knows? This is still day one of doing things a little differently. It may just end up being something faddish, which is something I  usually try to avoid, but when I see some potential in how it can help kids, I’ll dive head first. Sign in for yourself and try some of the later differential questions. Do you even remember how to do them? More importantly, do you know why? I’ll keep you apprised of how my little experiment goes.

When Statistics Mean Something

I just got back from a lecture featuring Stephen Dubner (coauthor of Freakonomics and Superfreakonomics). If you’re not familiar with those books, they try to strip away how we ‘feel’ about a particular topic (for example, teachers cheating on standardized test scores, or the hand hygiene of doctors in hospitals) and they address those sorts of topics “with neither fear nor favor, letting numbers speak the truth.” When we think of economics, we usually think of budgets, currency, the stock markets, etc., but what Dubner and his coauthor Levitt do is look at what some call ‘behavioral economics.’

A few things stood out in his talk. One was the reminder about how we are much more able to perceive traits (good and bad) in others than we are at seeing them in ourselves. Another is how hard it is to change human behavior. Finally, when collecting data, how you collect it is really important. Self-reported data, according to Dubner is usually pretty useless (especially if you ask people on a survey to identify themselves – even as a group). He gave an example of a headline that went something like this: “Recent survey shows that favor of nuclear power has declined.” Hmmm, a survey taken right after a tsunami destroying a nuclear reactor. Dubner mentioned how these surveys/polls are everywhere and those are not the kinds of statistics he is attracted to.  He also warned everyone about using incentives to try to change behavior. They have a tendency to backfire. Dubner also made a case for thinking outside the box. “Be a heretic,” he said, “but remember that most were wrong, many were executed, however, those who were right and lived, changed the world.” In terms of education, this talk reminded me of the importance of keeping our rigorous curriculum balanced between learning basic skills and fostering natural curiosity and creativity. For me, It was interesting to compare his talk with that of David Brooks who I saw last week when he was in town promoting his book. I was fascinated by many of the similarities.

Speaking of numbers, if you haven’t visited the site Gapminder by Swedish Statitician Hans Rosling, you really ought to. Can numbers be fascinating? They certainly can, and he does an incredible job on his interactive website which visualizes the data on world development. He’s done numerous TED talks advocating that one of the ways to stave off world population growth is to create wealth in all nations. His latest talk “The Magical Washing Machine” is only about 6 minutes long and well worth watching till the end when he makes his point. It makes me want to take more statistics courses.

 

Math is a Fine Art

This weekend, I read the book A Mathematician’s Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Artform by Paul Lockhart with a Foreword by Keith Devlin. It starts with this quote from Antoine de Saint Exupéry:

“If you want to build a ship, don’t drum up people to collect wood and don’t assign them tasks and work, but rather teach them to long for the endless immensity of the sea.”

In the foreword, Devlin says that “It is, quite frankly, one of the best critiques of current K-12 mathematics education I have ever seen.” He recommends that every policy-maker, educator and parent of a school-aged child with any responsibilities of teaching mathematics should read this book.

We’ve all seen children humming songs without care to the key that it’s in or how that song might be notated. We’ve also seen children take paints and crayons and experiment with the different media before they are taught about line, color, tone and other aspects of art. Yet, in math, Lockhart says we do not allow children enough time to enjoy and play with math and we ought to do so. According to Lockhart, the current K-12 curriculum in almost any textbook series only teaches kids a series of steps in how to solve a particular type of problem, along with some special notation. As Lockhart puts it, the current system “[destroys] a child’s natural curiosity and love of pattern making.” He claims that math is “simple and beautiful.”

He gives an example  of a triangle in a rectangular box.

How much space do you think it takes up? How do you suppose you can find out?

What Lockhart laments about is that without teachers who understand the beauty of math, we don’t allow children to grapple with this problem long enough before we rush to give them the formula 1/2bh.  If we allow kids to ‘play’ with this puzzle, they may actually discover it themselves.

 

Children will delight when they discover that by drawing a vertical line from the tallest part of the triangle, they will see that they have created two rectangles, and that the area of each triangle part is half of two smaller rectangles.

Today in class we were working with geo-boards and rubber bands. I teach second grade and the main objective was to create a variety of shapes with right angles to measure area (in square units) and perimeter (in units). When one student, who clearly got the concept was done early, I asked her to play with this puzzle for a while. I built a 3X2 rectangle and a triangle inside it. I asked her to think about how she might find the area of the triangle. After about five minutes, she lit up and with much excitement explained that she could divide the shape into two smaller rectangles and found the area of each one to be half of the rectangle. I asked her to try with a different rectangle and triangle, and her response was instant. What I didn’t give her was the traditional formula. She had basically discovered it on her own without realizing it.

Remember, I teach second grade, so this was exciting for me too. With the other children, some were excited in discovering the area of a rectangle to be the base multiplied by its height. This too was a discovery for these students and the joy of math was evident. I also did not provide a formula for them even after their discovery.

There are many critics to Lockhart’s point of view that it took centuries to arrive at many mathematical theories. He would argue that math which is rich “has been reduced to a sterile set of facts to be memorized and procedures to be followed. They are given the formula: Area of a triangle = 1/2 b h and are “asked to apply it over and over in exercises…By removing the creative process and leaving only the results of that process, you virtually guarantee that no one will have any real engagement with the subject…By concentrating on what and leaving out why, mathematics is reduced to an empty shell.”

Finally, here’s one last quote: “Math is not about following directions, it’s about making new directions.”

In the next few weeks, our school is about to go through a selection process for a math curriculum. While I empathize with Lockhart, there also needs to be a balance. I hope that when it comes time to discuss and debate the pros and cons of each math curriculum, we keep an open mind to process, discovery, and relevance, rather than what’s easiest to implement or what is an efficient way in transmitting a set of rules for practice and compliance.

Anyway, the book is an easy read, very compelling, and makes you think. Whether or not you agree completely with the author’s point of view.

 

Kahn – Flipping the Classroom

Of the TED talks given last week, this is the one of the ones I was anticipating the most. Human interaction is crucial to learning, but that interaction is just part of it. Can a robot or youtube video do my job? Only if I stand in front of the class the whole time and lecture. Sure, listening is an action, but doing something more interactive like student-student or student-teacher is a much more valuable use of their time. I had a few colleagues come back from the NAIS conference recently and really liked Sal Kahn both as a speaker and what he had to say. It really shifts the paradigm of traditional schooling, but as an educator, it also makes sense in many ways. I still need to explore Kahn Academy’s website and materials more thoroughly, but after this talk, I’m convinced I really need to. Best of all, it’s all free!

CCL – Are Roman Numerals Obsolete

I’m not sure who still uses Roman numerals. I learned them when I was in elementary school. I remember seeing them at the end of movie credits growing up, but that’s long gone. They’re still on the clock tower that houses Big Ben in London, but I suppose one could tell the time on a clock without numbers anyway. I haven’t even worn a watch in the past 5 years. Where else are Roman numerals used. I also thought of using the word sestercentennial in the title of this post, but it’s my 250th post, not the 250th anniversary of my first post.

We’re going to start learning about Ancient Egypt in my class, and I was trying to figure out what exactly the objective would be when we learned about the Ancient Egyptian numerals. It led me to think about when a certain tradition or practice ends and is replaced by something else, in essence, change.

The world is changing rapidly, but is education keeping up? We just had a week off for mid-winter break, and it’s given me time to pause and reflect about a lot of things. This week also gave me the time to figure out how twitter worked, and how it could help me stay apprised and connected of what was going on in the world without cluttering my inbox or remembering to check the various blogs I like. With twitter, I was able to follow two of my colleagues (since they tweeted) among many others I didn’t know who were eager to share what they learned at the NAIS conference last week. Even though I was unable to attend this conference in person as I did last year, being able to follow it gave me the renewed energy and optimism that I had after last year’s event. I don’t know why I hesitated to use twitter. It took thousands of years for Ancient Egyptian numerals to be replaced, but these days, companies that were once on the cutting edge seem to fade before one even figures out how to use it.

The week before our break, our Head of School gave us an article to read titled, “Why a School Doesn’t Run – Or Change – Like a Business.” Written in 2000, many of its points hold true a decade later. The article mentions the difficulty of change for many reasons. The author mentions that while teaching “benefits from regular refreshers and occasional overhauls, it doesn’t demand the kind of continuous updating that, say, law or medicine or high technology do.” A decade ago, I would have agreed with him on this note, but change in education, however slow it may seem to some is inevitable. The difficulties still remain, and school leaders must approach change with clarity, focus, and continuity while respecting educators’ motivation and innovation. The change has to be clear and articulated well. Educators can support change if the ‘why, what, and how’ are addressed. They can support change if it doesn’t mean “do more,” but instead means try doing things differently. Finally, a very important thing he mentions is that educators need to know what won’t change, so they can rely on some continuity.

If the objective of learning about Roman Numerals provides kids with different ways of thinking about numbers, it’s good enough for me and should still be taught. I’m sure our Latin teacher can give me at least X number of other reasons why.

I was going to write about a few articles I read today: George Will had an interesting column about Teach for America. Daniel Pink had a column about detesting the question, “What’s your passion?” Both David Brooks and Paul Krugman have chimed in on what’s going on in Wisconsin as have many others, so I’ll spare boring you with my two cents. You can read the articles by clicking on the links. There’s a lot to write about, but the Oscars are about to start, and I’m sure I’ll have something to else to say soon enough.

 

Math is Not Linear

Math is often taught in a linear way, and each new year, students revisit topics and build upon them with the ultimate goal at the end of high-school being calculus. Geometry plays a big part, and I remember all kinds of min/max calculus problems involving solid shapes. But what strikes me, is how little the topic of statistics is taught in the K-12 setting. Many who graduate from college are not going to use much of the higher-leveled math in their careers, but they will be exposed to a lot of data – and they should be able to recognize when this data gets misrepresented in the news. When someone reads something that begins, “research says…,” do they understand those numbers and what they mean? Can they recognize a graph when it’s skewed to favor the author’s point of view? Infographics are some of the best visual ways of trying to convey data, but some of them are simply just beautiful art and actually quite misleading. Some, of course, are brilliant.

This week, the New York Times had an article titled Teacher’s Colleges Upset by Plan to Rate Them. The U.S. News and World Report has told many colleges to comply or they may simply get an F rating. Even though many of the colleges (including Columbia, Harvard, and Michigan State) have all stated that the measuring systems are flawed.

This week’s New Yorker, has a piece by Malcolm Gladwell also criticizing the U.S. News and World Report for its general ranking of schools. Honestly, how can you compare apples to oranges? And yet they do. When you factor many of the measurements: endowment, scholarship, tuition, graduation rate, and so on, how do you give each of the measurements equal weighting?

And yet, for some reason, people would rather not think about all the different numbers. They want a nice little number that they can use to order the schools. The U.S. News and World Report admittedly says that the way they weigh its metrics aren’t scientific in any way. Obviously, not a reliable source, yet their publication sales continue to rise.

When measuring teacher effectiveness, the same kinds of things must be considered. How much do you weigh experience, achievement in test scores, degrees earned, anecdotal reputation, etc.? The test scores are a tricky one too. If you’re not comparing the same group of kids, you’re comparing apples to oranges. Furthermore, if you’re comparing one school to other schools, can you aggregate data such as financial aid, diversity, ratio of teachers to students, test scores, and so on. Again, we’re comparing watermelons to tomatoes. Local magazines love to compare schools in the city using data that’s usually dated and not very useful. They also like to come up with an aggregate score and rank schools.

I think some of the metrics measured are legitimate and should be looked at closely, but to give each of those an arbitrary weighting so as to come up with a single number for a ranking is not good math.

These past two weeks in second grade math, the children have been making paper quilts. While not a lot of statistics were involved, the children were employing their knowledge of measurement, area, perimeter, addition, multiplication, fractions, estimation, and problem solving. Not to mention that the quilts also lent themselves nicely to social studies themes like the Underground Railroad as well as integrated nicely with story telling.

So many math text books present fractions in a chapter midway through the year. In reality, fractions are everywhere. They’re in music, quilts, baking, Lego, and so on. Why wait to introduce the concept of ‘half’ midway through the year, when you can use it all year long? I guess I want my students to see the connections between fractions, and measurement, and the operations they need to use to solve problems involving those connections. Fractions aren’t something that exist in a vacuum. They’re part of these children’s world. It’s everywhere – and to wait until chapter 8 (or whatever it is in the book you’re using) is just wrong.

I know I meandered from the topic of statistics using fractions in second grade, but as adults, statistics are all around us. The data is often analyzed by ‘experts’, but we need to be able to do better than take someone else’s word for it or buy into the simplicity of an arbitrary ranking system. Malcolm Gladwell’s article in the New Yorker may seem obvious to many, but many are reading U.S. Weekly News!

The Importance of Art in Schools

It’s surprising and disappointing how so many schools choose the arts as one of the first department to go either when times are tough or when they are pressured to increase their scores on achievement tests. It doesn’t take one long to find that these cuts are taking place all over the country: Fort Lauderdale, California (and that was in 2006 when things weren’t as grim) (here’s a more recent story from CA), and even as recently as this past week over in the UK. At least according to the Obama’s art-education platform, it states that …”we should encourage the ability to think creatively that comes from a meaningful arts education.” This article about the exhibit from the Seattle Times talks about the links art has to “math, science, literature, you name it.” I feel extremely fortunate where I work. When they designed the new school building, they had several local artists contribute to a few pieces around our campus.

Yesterday my students and I had a great day of art. One of Seattle’s local artists, Juan Alonso who created 5 pieces of abstract art around our campus came to talk to the students about what inspired him and about some of the process involved. He also started giving workshops to classes on abstract portraits. I can’t wait until it’s our class’ turn. What I love about abstract art especially is that it is open to interpretation unless the artist actually tells you what inspired him. The sculpture on the right sits in front of our school. I always pictured it as the font of knowledge or something to do with passion. Juan Alonso explained that when he thought of an elementary school, he thought of a child with arms reaching upward. Now every time I see it, I can’t help but think of that.

After our assembly, four classes headed to the Picasso exhibit at the Seattle Art Museum. It’s the last week of the exhibit, and I have never seen the place that packed. Rather than battle the crowds and try to see all of it, our wonderful docent selected just a few. She had the kids full attention and began by asking them what they thought they saw. With this kind of open ended question, it was amazing how much effort the children spent looking at the painting, the colors, shapes, etc. and the thoughtful, yet out-of-the-box responses were inspiring. Asking children to inquire about art is no different than what we ask them to do in science. Much of the vocabulary needed to describe Picasso’s work is shared with geometry. Reading about his life and the times, learning about Spain and France, and writing about their experience are natural connections. Our docent was wonderful and asking the right kind of questions forcing the kids to think a little more critically rather than just come up with a one-right-answer response.

Of course, what I loved is that his art is celebrated for breaking the rules, for being a visionary and wanting to push boundaries in art, for leading change rather than following it, and working hard. Some of his paintings were based on hundreds of initial sketches. This exhibit also highlights someone who worked until he was 91. Noticing a couple of my children’s eyes light up when the docent pronounced that Picasso created his art as one would write a diary. You know the kids who want to draw before writing and those who prefer it the other way around. Why not celebrate both kinds of kids and be open to different ways of arriving at the same objective.

The children then took part in a workshop at the museum offered by a teaching artist where they created mixed media collages of portraits using the concept of viewing things from multiple perspectives. The results, though unfinished, were wonderful, unique, and more importantly something they were all proud of. Whether it be the performing or visual arts, schools must make room for it. Visual art promotes multicultural education, critical thinking skills, inquiry, creativity and innovation, math skills, science, literature, and so on.

The exhibit runs for just a few more days until the 17th of January and the museum has extended its opening times until midnight. This was one of those things that wasn’t part of the planned curriculum, but in my opinion, worth doing. It was my third time seeing this exhibit, and I was still awed. I hope some of the children were too. If you don’t mind crowds, you can click on the picture below which will link you to the museum’s website.

The Shadow by Picasso

Integrating Math and Literature

This month’s Teacher Children Mathematics journal had a great lesson involving the Caldecott winning picture book, Jumanji. Those familiar with the title know that it’s about a pair of children who find a board game and begin playing it by rolling the dice. Things get out of hand and the only way to end the game is by rolling a 12. Then (to a lot of groans), I slammed the book shut and asked the children that we were going to do some math and I would read the end aftewards. I began by asking them  how likely they thought the chance would be that a 12 would be rolled. There was a large range of answers. I then gave each child a pair of dice and asked them to roll it ten times and to record their answers. Finally, we took all their data and filled in a graph on the board. It looked like a nice rolling hill. I then asked the children why they thought this pattern emerged and eventually they started to say that the were more combinations of numbers to add to make 7 whereas there was only one way to get 12. We then read the end of the book and it was a great way for children to experience the concept of probability and how it might affect their lives. Would it be better to build houses on your strip of Monopoly when someone was 1 place away or 6 places away? Why?

Unfortunately, many textbooks are so linear, teaching one concept at a time, they don’t leave room for integration of other math concepts or even literature connections for fun, engaging, lessons like these that ask kids to discover the why behind the math. Many textbook series have ‘literature’ connections by producing their own children’s books. None to my knowledge have measured up to Chris Van Allsburg’s Jumanji – a true classic.

 

Making Data Beautiful

Making sense of student ERB test scores on a spread sheet can be daunting for some, and after staring at those numbers for a while, make one’s eyes a little blurry. Turning those numbers or any kind of numerical data into something more concrete, like a pie chart or bar graph makes it much easier to read and grasp. Taking it one step further and pairing up with other data could reveal some interesting patterns. For example, with the test scores I mentioned, when comparing them to other schools, what if we were able to include data on the size of the school as well. Would the results change? What is the statistical significance when comparing a school with one class per grade to one that might have 10 classes per grade. Does the sample size change the data set in a way that might be interesting? There are many other ways one can think about data and there has been quite a rise in what is called an infographic: taking the data, adding some design to it, and representing it in a way that can be visualized so it can be easier to understand.

In his TED talk below, David McCandless draws interesting conclusions from complex datasets and pairing them together. So instead of looking at simply what country has the biggest military budget, he might pair that with the country’s GDP and suddenly, the results are quite different. He also has a blog worth checking out called Information Is Beautiful. It’s definitely worth checking out.

 

 

 

Forced

One of my goals this year is learn more about gardening. My kids have a garden journal and I’ve decided to blog every time they make an entry. Descpite 14 degree weather, the green fertilizer we planted continues to grow. I learned that because it snowed first, the snow acted as an insulator and therefore there was no frost.

In the classroom, we decided to force bulbs. After following a sequence of instructions, I asked the kids, “Where’s the math?” and here are some of the responses I got:

“You had to measure out 1/2 a cup of water and 1/2 a cup of sand, so there was measurement and fractions.”

“You can measure the height as it grows and graph it. I’d use cm because that’s what scientists use, but I suppose you could use inches too.”

“We can estimate how many days until the first bloom.”

“We can find the difference in height between two different groups.”

The list continued.

This might not be math the way text books teach it (which tend to be linearly), but it certainly makes math meaningful to children because it’s tangible and kids can relate to it.

I haven’t told the kids yet, but there’s a literature tie-in too. Later in the year, we do a unit on Greek myths and they will be able to relate to the story of Echo and Narcissus.

Which Came First: The Paper or the Computer?

For the young children we educate now, they arrived into this world where both existed at the same time. This “TED talk” below features Conrad Wolfram trying to change the paradigm of how math is taught. If you’re familiar with him, he’s the man behind the website Wolframalpha. It’s quite a fascinating website. If you’re a math nerd, or even a teacher wanting to make math relevant to kids, it’s a great website. Just type in any equation like “2+2” without the quotation marks, or “2,5 torus knot” and see what you come up with. Then get crazy and try entering your birthday or an historical event.

For those of you who remember the quadratic equation, ask yourself when was the last time you used it. More importantly, if you do remember it, ask yourself, how, why, and when you would use it? I think I’m safe with 2nd grade math, even though it’s important to stretch kids in every possible way. For middle school teachers and beyond though, he poses a very good argument. One thing I certainly agree on is that we all need to support kids with estimation, reasonableness, and mental math strategies. It’s well worth the 18 minute video, especially if you’re interested in math ed. reform in this country. Alternately, with TED talks, you can click on a link to get the transcript, if that’s your prefered method of learning.

Here’s the blurb from TED about the following video titled, Teaching Kids Real Math with Computers.

From rockets to stock markets, many of humanity’s most thrilling creations are powered by math. So why do kids lose interest in it? Conrad Wolfram says the part of math we teach — calculation by hand — isn’t just tedious, it’s mostly irrelevant to real mathematics and the real world. He presents his radical idea: teaching kids math through computer programming.

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Knowing What AND How to Teach Math (then reflecting on it so you can do it even better next time)

The November issue of Teaching Children Mathematics features 3 very good articles. The first, “What Knowledge does teaching require?” by Thames and Ball mention that a clear description of such knowledge in research over the past 40 years has been rather elusive. Just because you know a lot of math or can do math very well, doesn’t mean you can teach it well. Of course, the authors do not doubt that you have to have a good grasp of mathematics. Whether you’re a math major, however, does not make a difference according to their findings. What they argue is that teachers need to “uncover the mathematical issues that arise in practice. By better understanding the mathematical questions and situations with with teachers must deal, we would gain better understanding of the mathematics it takes to teach.”

They broke up what they called, “Mathematical knowledge for teaching” into several domains in relation to teaching. There’s “subject matter knowledge (SMK)” and “pedagogical content knowledge (PCK).” Each of these two can be divided further into three sub categories each. SMK can be grouped into these three: common content knowldedge, knowledge at the mathematical horizon, and specialized content knowledge. PMK can be grouped into these three: knowledge of content and students, knowledge of content and teaching, knowledge of curriculum.

The authors also mention that these are some math skills good teachers or mathematics need:

• posing mathematical questions
• giving and appraising explanations
• choosing or designing tasks
• using and choosing representations
• recording mathematical work work on the board
• selecting and sequencing examples
• analyzing student errors
• appraising students’ unconventional ideas
• mediating a discussion
• attending to and using math language
• defining terms mathematically and accessibly
• choosing or using math notation

Just today, we introduced the children in my class to base 4. The purpose is to solidify the concept of place value and to understand the construction and deconstruction of numbers so that the children have a better understanding when taught the traditional algorithm. Just going through the list above, we did several things differently from last year. This year, I chose to create something that we could represent on the board. It made a huge difference – not only in understanding, but in engagement. Of course having kids interact with the board was great. So what if the architects decided that the board had to be a minimum of so many feet off the ground, I stuck a chair nearby and those who needed it, could step on and still reach. Letting the children give their explanations as to why they were rounding up groups of 4 and putting them in the next column seemed to help a lot too. Posing questions was also great. About halfway through the activity, one of my students raised her hand and said, “I think that with the materials we have here, the highest number will be 133.” She was absolutely right.

This article says that mathematical knowledge in the way that is required for reasearch in mathematics is not what is needed. What is needed is someone who has excellent “mathematical knowledge for teaching which itself is a kind of complex mathematical understanding, skill, and fluency used int he work of helping others learn mathematics.”

The second article, titled “Balancing Act” focused on high-quality professional staff-development. First of all, that development needs to be ongoing. According to the author, it needs to be focused on three essential things:

1. Content focused on instructional design and implementation
2. Process characterized by inquiry, observation, research, and collegial interactions
3. Contextual support for job embedded professional training

This development has to be long-term and sustained in order to make a lasting change. If you think about those three criteria above combined with the need to customize learning to the needs of each individual student, there is no way that two classes will ever be the same, and while a textbook may be a useful tool at times, one must resort to using other tools as well. The author of this article says the challenge is to find the time to collaborate and reflect on what worked and what didn’t. The author goes on to say that textbook providers tend to provide training to teachers once they’ve purchased their materials, but that training goes away after a year or two and teachers, especially new teachers, need continual training. Another challenge that lies in changing how math is taught is the resistance many teachers have to changing what they’ve been doing for years. I have always been open to change, but I have to admit that I am resistant to thinking that a new textbook alone can be a panacea to improve the teaching of mathematics. You need to also know HOW to teach it.

Finally, the third article from this issue I liked was titled, “A reflection framework for teaching math” by Merrit, Rimm-Kaufman, Berry, Walkowiak, and McCracken. While these authors offer a guideline with 8 dimensions in their “framework for reflection, not every lesson will be ‘high’ on all dimensions.” Below are their 8 dimensions. As one reflects on a lesson, here is what to consider:

1. Lesson structure
2. Multiple representations
3. Mathematical tools
4. Cognitive depth
5. Mathematical discourse community
6. Explanation and justification
7. Problem solving
8. Connections and applications

After we finish working in different bases in my class, we will move on to addition and the use of traditional algorithms. There are some children, solid in their understanding of place value, who already know how to use the traditional addition algorithm where you carry (regroup) into the next column. If these children have already mastered this, how do I extend their learning while teaching the rest of the children the traditional base-10 algorithm for addition? At least I’ll have until after Thanksgiving break to ponder this.

My opinion on why so many districts have failed to implement a textbook series successfully is not because of the content within those books (as I mentioned they make a nice tool – and there are many online tools available for free, if one is willing to take the time to find them), it is because there hasn’t been sustained development in making better teachers of mathematics regardless of the text or tool. Whether it be Everyday Mathematics, Singapore Math, or other programs (each has it’s pros and cons), it boils down to how you use it with your students. The concepts behind the math may not have changed over the years, but the way we teach it, engage our kids, and make it stick certainly have.

 

I Have a Hunch…

…that Education is going to change quite significantly before I reach retirement. Does anyone else feel that way?

I just finished two books this past weekend: Steven Johnson’s Where Good Ideas Come From: The Natural History of Innovation and Ken Robinson’s the Element.

Both books are about creativity and innovation and what is unsurprising is that there are many similarities between the two books.

What I liked about Robinson’s book was his idea and definition of creativity. There are multiple modes of intelligence and he provided great examples from fields other than the arts (even though he is a strong proponent of giving the arts the same importance in schools as reading and math). He talks about a Nobel winning physicist. Richard Feynman, who found his passion, but is was almost by accident, some serendipitous moment, where he started to play with ideas just for fun – think of google’s 20% free time model, and then saw a connection that eventually led him to his prize in quantum electrodynamics.

Johnson also claims that there are many ways that good ideas spring forth, but the solitary eurika moment is very rare. Usually it begins with a hunch and it’s some other event, or somebody else’s hunch that triggers the new idea. Two half-hunches, if you will.

One thing Johnson mentions is that our abilities to connect with one another through technology has increased tremendously, and that as you can see from wikis and the idea of open source technologies, people are coming up with new ideas faster than ever because of the possibility to connect more.

I posted his TED talk earlier where he described the ‘invention’ of GPS as a side project (again like google’s 20% free time to pursue your passion project). Eventually Reagan allowed that satellite technology to be ‘open source’ and many of us now have devices in our pockets that can locate the nearest Starbucks.

All too often teachers teach math or writing to children like there is only one right answer or one right way to do something. Standardized tests (while they have their place) reinforce that. It’s clear Feynman didn’t see math that way. He didn’t know what he was looking for until he discovered it. The ‘inventors’ of GPS didn’t start out trying to design a geo-location device.

The bottom line is that being open to new ideas may allow your half-hunch to become complete. Children need to learn to work with one another and collaborate. They need environments where the diversity of ideas spawn new and better ones. They need to be part of a working community full of people who are passionate about what they do.

If you want a short taste of Johnson’s book, below is a quick 4 minute animation from a recent keynote.

Oh, and is it too late to find your passion or your element? Robinson gives many examples of people who found it well after they turned 40. And if you have a growth mindset, that shouldn’t surprise you.

One Way to Differentiate and Spiral Several Math Concepts

It’s rare Seattle reaches 65 degrees in November, and on this beautiful fall day, the children went and harvested beans from a nearby garden. They worked in teams of 4 and 5, had different jobs and had to agree upon them before we left.

When they returned they did some estimating (how many beans in the pod), and began to measure the length of each bean. And some groups began to graph the length of their beans. Reviewing how to use a ruler, asking what is the difference between cm and inches and how do you know, creating a graph, as well as what a key tells us on a graph were some of the objectives laid out for them.

Tomorrow, they will continue by finishing their graphs and begin to weigh the beans they harvested. Again, they will get an opportunity to graph these beans by their weight. They will also use their graphs to generate word problems. Some will need templates, other children will be able to come up with very sophisticated problems that I probably would have never thought of myself. That’s the fun thing about open ended math activities.

Furthermore, we will tie it in with the story of the bean farmer and how the Pike Place Market started in 1907. We will also take the pods and compost them in our school garden’s compost that we started this year. If time permits, a story about Jack and Beanstalk should be included too, as the 2nd graders work on fractured fairy tales later in the year. Fairy tales are hard to fracture if you’ve never heard the original.

Next week the beans will be cooked and the children will follow a recipe (a little more measurement here too) to make bean dip, learn a little bit about nutrition, trying something delicious, and have a fun time doing it.

These are the kinds of lessons that are so important in elementary school so that math, language arts, social studies, science, etc. is not taught in a vacuum. Yes, they will need foundational skills to measure length and weight, and some may need more direct instruction for some at remembering how to create a bar graph. Whatever the skill, it’s important to assess how the kids are doing by getting right in there and using that assessment to guide your teaching so that, like the beans, the children can grow.

Some people think of spiraling as 10 questions at the bottom of a work page that asks questions that may include items one needs to review. The activity above has that all built in, but there are more places to differentiate in an activity like the one above.

Here are some examples how one can differentiate just through questioning:

How long was your longest bean? Use your graph.

If you put all the beans your team harvested end to end, what would the total length be?

If your team managed to harvest 3 times the amount you did, how many bean pods would you have?

Make up your own question using the words total, weight, and graph.

 

Multiple Perspectives

I had the fortune to visit the Museé National Picasso in Paris years ago and perhaps aside from the Museé D’Orsay, it was by far my favorite museum. For a couple of reasons. Firstly, it was in a house and very intimate compared to the immense Louvre or Pompidou, and secondly, because it contained works from his own collection that he never sold, works that were personal to him. Also, these works spanned all the different periods this one artist had. Without a doubt, he was an innovator.

Well, as the museum in Paris undergoes some construction, Seattle, is one of the few cities that is showcasing this work and we are fortunate to take our kids to the exhibit in January. The SAM is an excellent resource for educators and they have put together a great website full of great resources including audio guides as well.

Today, there was a workshop for educators which included several activities, a tour of the exhibit, and learning how to integrate art into your curriculum. The Susan Brotman Deputy Director for Art and Curator of European Painting and Sculpture, Chiyo Ishikawa provided a lecture on the man’s life and periods as well. I like hearing her speak about art at anytime.

I have to say that the education department at the Seattle Art Museum is excellent, as I didn’t just learn about the art and artist, but they also teach it using different strategies that one can bring back into the classroom easily.

It was a very different experience seeing the same work on large white walls, but I still was in awe of his constant pursuit of something new. When asked, how does this relate to your curriculum? The evidence was everywhere.

Relationships – besides his many female companions and muses, Picasso entered his blue period in part because of the suicide of a very close friend. This plays directly into our social and emotional curriculum. One teacher from another school, told my colleague, “You teach Second Step? – well use some of his images to elicit empathy from your kids.”

Identity and expressing oneself – we ask kids each day to look at themsleves and look at the differences that make them unique. What are their strengths? What are things they need/want to work on? An artist, writer, musician, or dancer, etc.  often puts a lot of his or her emotions into their work and then displays it for all to see. Picasso was also moved to make political statements and his response to the German and Italian bombings of Guernica, his piece of the same name (not in this exhibit, but in Madrid), is a fine example of political and expressive art.

Growth mindsets – although Picasso was an art prodigy, he resisted the status quo and pushed himself to pursue what he believed in. He pursued excellence and worked hard. While he died a very rich man, he was not always so, and as studies suggest, effort more than ability, is what matters – and kids need to be praised for their efforts.

Innovation – This one is obvious. But innovators often go against the status quo, and it did not deter him from trying new things.

Those are just the big ideas, but the there were plenty of day to day curricular extensions. Social Studies, Science, Math and Language arts were the focus. I was with a group of lower elementary teachers whose task it was to create a math activity using one of his works. Geometry was an easy choice, but we picked a piece called Sacre Couer (which you can view here – due to strict copyright laws, they asked us to save certain images for class use and then view it online otherwise). We were given this lesson plan from the museum as a guide. We focused on the main objective being that kids would learn about 2D and 3D plane and solid shapes and how to do that on a flat surface. What struck me is that as some of use talked about using other global landmarks, or their own community landmarks to deconstruct, and started to think about some of the bigger ideas and concepts of critical thinking, problem solving, innovation, how to get kids working collaboratively, etc. a few teachers were very emphatic that those things didn’t get tested and therefore were not important. Their school would either be rewarded or punished if their kids did not perform well on a test. This sent shivers down my spine as I feel very strongly that skills beyond the basic recall of information, but that is the reality that some schools face. The museum even included a copy of the Global Competence Matrix in our package. You should check it out. It’s well worth it.

Anyway, the results from all the different groups produced some good lessons that were all adaptable and covered a wide range. One group who were high school teachers took a quote from Picasso, “Art is not made to decorate rooms. It is an offensive weapon in the defense against the enemy,” and used it as a way for kids to use art to make a statement. That same kind of thing could be done with younger kids and how it relates to bullying, for example.

My favorite quote was, “Painting is stronger than me. It makes me do what it wants.” I’d turn that around and ask can teaching be stronger than you? For me, the answer is yes. There are some days where the best laid plans go out the window and you try something new because your students are craving it and they couldn’t care less what was in your plan.

The theme of the day was multiple perspectives. Whether that is what you think of when you think of Picasso’s work, look at art in a mathematical way, or have personal and cultural perspectives of individuals influence a collaborative effort, Picasso can teach us and our students a lot. I have never seen the museum so busy before and am glad that this exhibit is a great success.

I’m looking forward to our field trip there in January.

Again, in Math – It’s About the Process

Later this week I get to sit down with parents and together set some concrete goals for their children. It’s a great process as it allows us to focus and target as well as individualize what we think will be most beneficial to a particular child. To increase success and motivation, I would even include the child in setting their own goals.

Our faculty also sit down with our administrators and have a goal setting meeting and I only had one goal this year – to get better at what I do.  I then broke that one goal out into little goals, and I really don’t know how my one goal morphed into four pages – especially when my first bullet point was to simplify things. Nonetheless, I still only have one goal – to grow as a teacher. Anyway, one of my ‘sub-goals’ if you will, was to read one article from Teachers of Mathematics a month since math continues to be an area of curricular focus for our school this year.

The one I picked from the October issue was called Building Word Problems: What Does it Take? by Angela T. Barlow.

The first question asked by the author is why would we create our own problems when there are text books and other curricular materials out there. The reason is pretty simple. Because those materials (while they have value) were not written for every kid in mind and creating your own problems allows you to customize learning. Furthermore, many of those problems focus on a single strategy vs. having kids use what they already know. The authors also say we need to thisbecause “future citizens must be prepared to problem solve and apply their skills to new situations.” According to the article, there is a process involved that requires careful thinking. Here’s the process:

1. Identify the mathematics goals.
2. Decide on a problem context.
3. Create the problem.
4. Anticipate students’ solutions.
5. Implement and reflect on the problem.

Every morning when the kids come in to school, as they are settling in, I have a math problem on the board. Increasingly, I’ve tried to make the questions more open ended or focus on the process involved. I thought I’d look at the process above and reflect on it here.

The goal was to add two two-digit numbers together, use a variety of strategies, have kids explain their thinking, not rely on algorithms that haven’t been taught, and perhaps get children to round numbers.

The context was just for them to be able to communicate their thinking.

The problem (not very creative) was something along the line of “Add 99 and 99 together. Explain your thinking.”

I anticipated many of my second graders to struggle with this one. I had used it much later in the year last year and noticed kids immediately relying on the traditional algorithm they had learned. Not that there’s anything wrong with that (algorithms are great tools, but they don’t always reveal how one thinks about numbers).

With some children I prompted with further questions like, “is 99 close to a number that’s easy to work with?” Many of the children didn’t hesitate, they tried to use what they had to solve the problem.

With that question, one child said, “Oh, 100 plus 100 equals 200 and you just have to subtract 2 to get 198.”

Another child said, “Well you just add 1 to 99 to get 100. Then you add the 99 to get 199, but don’t forget you have to take away the 1 you added, so the answer is 198.”

One child said they knew 90 and 90 was 180 and that 9 and 9 was 18. They couldn’t seem to add 180 and 18 together, so he just deconstructed it and said, “180 plus 10 is 190 and 190 plus 8 is 198.”

It’s not the greatest question, but it’s really nice to see kids grappling with two-digit addition long before we introduce them to the traditional algorithm. Not only is it promoting good number sense, but it also promotes creativity. They are not relying on a single strategy from a text. They are in fact teaching themselves how to solve a problem. They are becoming more resourceful. Upon reflection, the problem could be asked in a better way, but the outcome for most was a positive one.

 

You Can’t Hurry a Garden

…or children for that matter.

Keeping with Yong Zhao’s children are like popcorn, it was clear to me last week that some children weren’t ready to pop. We took a ruler out to our garden plot and decided to measure the rye grass and got a range from about 8 to 14 cm. Why cm instead of inches, it’s scientific, global, and in the common standards. What I tried to do was have them make the height of one box equal 2 cm. While half my class was ready to make that leap, the other half were still a little confused.

It was a good lesson in trying to remember where the kids are and not jumping to where you want them to be. I know growing a garden alone isn’t going to raise test scores, but it has the potential to definitely teach the children all sorts of great values about nutrition, agriculture, sense of community, the science of soil, nutrients, and plants, as well as data collection, measurement, and a whole host of other kinds of learning. Some of these activities may actually be useful in a test.

This week we visited our garden plot again, after reading Demi’s The Empty Pot about how honesty can be a courageous act. As a follow up to that reading we asked the children to remember what our master gardner said about each cover crop and what ‘trait’ each one had. The vetch was shy and would be the last out. The rye grass was tall and bold. The clover was friendly and loved to spread around. The students added to these traits, made one or more of these a main character and wrote a story.

What Vetch might look like when it's all grown up.

This time with careful guidance, the garden activity was meaningful to all and they came up with the cutest stories. It was a great way to teach about setting, character and plot through our garden.

 

Doers of Mathematics

I’ve blogged about process quite a bit, but there’s a great article in the September issue of Teaching Children  Mathematics titled “From the Inside Out” (by Fillingham and Barlow)

 

Children vote on liking or disliking a vegetable and then work in cooperative teams to create graphs.

about what motivates kids intrinsically to become “doers of math.”

The article notes that it isn’t sufficient simply to look at the National Council of Teachers of Mathematics (NCTM) process standards, but to actually observe the behaviors and interview the students to find out what makes math so exciting and fun for them. Just doing it, isn’t enough. This journal is published by the NCTM.

There are some regular classroom motivating factors . But we must look at their own personal motivations. The authors of the article notice three behaviors emerge.

1. Connecting to previous material.
2. Responding beyond the original question.
3. Conjecturing or predicting with relevance to mathematical discussions

Students will engage in these behaviors without prompting if actively engaged. How do we get more students to be this engaged? Teachers need to model the desired behaviors, and this can be done through simple open ended questions:

How does this task relate to ____?

What would happen if______?

Teachers should acknowledge the behaviors when they observe it, use student work as exemplars, and can also ask questions like:

Do you agree or disagree? Explain.

Is your response similar or different?

How is your response similar or different?

Finally, the article concludes by saying that it’s not our job to force kids to move from extrinsic to intrinsic motivation – you can’t do that – but to create an environment that enables kids to initiate their own behaviors as doers of mathematics.

In the picture above (from this year’s 2nd grade vegetable taste test), the image shows a station where children try a vegetable and then vote yes or no using a red or green unifix cube. They are familiar with the process as they have done it since Kindergarten. However, the progression from K to 2 is that they begin in K by voting on just one or two vegetables and the whole class creates one or two graphs. By the time they get to second grade, they taste 6 different vegetables and work in cooperative teams to create 6 separate graphs. They then are asked how their graphs are similar, different, what worked, to make up questions related to their graphs, etc.

They are definitely becoming doers of mathematics.

This article and video from edutopia features how to teach math as a social activity, and fits in line with the article mentioned above.

Singapore Math Adopted in More U.S. Schools – NYTimes.com

Singapore Math Adopted in More U.S. Schools – NYTimes.com.

This article is an interesting one. As we continue to look for ways to improve math education in our school and across the country (this is a national issue), Singapore Math creeps up again and again.

We use manipulatives daily and go from concrete to visual to abstract in almost all of what we do daily. The objective for the teacher is for the student to understand the math objective for the day. You can learn so much from a child by just asking a few questions, and you can differentiate fairly easily in math. I really believe that ambiguity in math, rather than the ‘one right answer’ approach helps kids develop better thinking about our number systems.

It was nice to get to the end of the article and see that it mentions a 2nd grade class using dice and building two and three-digit numbers. We did that all of last week in a variety of ways to help the kids understand place value. But there are other ways too. Using different base systems, for example.

99 may be 9 tens and 9 ones, but it’s also only one less than a hundred, and sometimes that is really more useful. The latter is not often taught and this year, I am trying to get kids to think about numbers in many different ways. Playing with math is what makes it fun. It’s not about getting right and wrong answers – it’s about the process in how to get there.

I’m looking forward to my little experiments this year and adding more ambiguity to some of our math, so that kids become more comfortable with numbers.

Making Math Meaningful for All

I finally got a chance to dig into my copy of Education Leadership and several articles have already grabbed my attention in a good way. I was glad to see a an article about differentiating instruction in math and some easy ways to do it.

If you’re an ASCD member you can get the article here, but I’ll try my best to summarize or feel free to borrow my copy when I’m done. I also saw one floating around in our faculty lounge.

The article is titled, Beyond One Right Answer and criticizes that math is viewed by too many students as something to answer quickly with an answer that is expected by the teacher. First of all, two widely held beliefs need to change:

1. That all students should work on the same problem at the same time.
2. That each math problem should have a single answer.

Two core techniques are discussed in the article. They are not new, but every teacher of math should be aware of them: using open questions, and parallel tasks.

Open Questions

The easiest way to create an open question is to provide the answer to the students and have them challenge themselves to make up the question. At first students can be uncomfortable with ambiguity, but they will warm up.

Another strategy for open questions is to ask for similarities and differences. Ask students to give two examples each of how 4 and 9 are similar and different.

Yet another strategy is to allow choice in the data provided before solving the problem.

Finally, ask students to write a sentence. Give certain vocabulary they must use, but have them design the statement.

Parallel Tasks

These are tasks that focus on the same big ideas but have different levels of difficulty. I remember that each year, we do a quilting unit and when asking kids to describe how they figured out how many quilt blocks were used, we received different suggestions from repeated addition to some kid multiplying the width by the length (we don’t teach the formula for the area of a rectangle in second grade, but it’s exciting when kids discover it on their own).

One way to create a parallel task is to let students choose between two problems. The same concepts could be covered, but one of the questions would be more difficult than the other.

A second strategy is to pose a common question like “what operation would you use to solve that problem?” or “Can you solve this in your head?”

Math is not something you train kids to do like a pet. It’s something that should be explored, discovered, played with, and made real.

Great Article in NYtimes

The most read article today in the nytimes is titled: Forget What you Know About Good Study Habits. (it came out on the 6th, but I’m only getting to it now. I haven’t read an ed. article in a while, but this one really struck me.

It reinforces the importance of integration, scaffolding, and moving children around. It also highlights that there is not one single right way to do anything, but there are good and better ways to learn. It also mentions motivation and growth (two things I’m really interested in).

I like this graphic accompanying the article by Ellen Weinstein.

This week all my students sat next to a different person each day. This week we conducted lessons at their tables and on the floor in the classroom, outside around our school building, and in the hallway, just to mention a few places.

The three R’s at our school are Respect, Responsibility, and Resourcefulness. I also hope to add Resilience, Rigor, and Relationships. Also very important life skills.

Now, on to some non-educational fun magazine reading.